Real life systems such as communication, social, biological can be described with the help of complex networks [1]}, [2]}. It is a challenging task to design a time-varying communication network (TVCN) with the ability to respond to the randomly changing traffic. Hence, the study of the traffic dynamics and fair sharing of resources on communication networks has received a great wave of interest for the researchers in past few years. The allocation of resources among the users in an unbiased manner is one of the challenging tasks in today's scenario. For assigning resources in an unbiased or fair manner, some researchers use various rate vector allocation schemes [3]}, [4]} to gain maximum utility while others select fair end to end window-based congestion control scheme [5]}, [4]}. In this paper, we are interested to design a TVCN model considering network growth, redistribution of traffic from heavily loaded nodes and removal of some fraction of links to reduce maintenance cost. A window-based congestion control scheme may be applied on the proposed TVCN model and user's current window size may be updated by considering delays(communication, propagation and queuing delays).
